When I was in an undergrad class I learned wwts, meaning 'we want to show'. It was new to me at the time, but I have used it since with my own students. Looking at current abbreviations, I think it works better than what Dr. Peyam uses here which is distracting to students.
I love how I'm not the only person that was completely thrown by 'wtf' hahaha! Absolutely love the dedication and quality content Dr. Peyam we do not deserve such an amazing prof. like you!!!
My calc teacher gave a good intuition for line integrals. ds becomes ||T'||dt because it's the speed*time, so you get a tiny distance. The function is at a certain height, so distance*distance is area. Adding all the tiny distances together you get the integral. Same sort of things for vector line integrals, except it's F•ds = F•T'dt.
Hey man just wanna appreciate your work, I have been watching your videos since I was in secondary school now I'm about to pass out of college and still proceed to watch your videos with same enthusiasm whenever it pops up in recommendation, just can't resist watching.
Alternatively, you could also express y in terms of x. --> y(x) = sqrt(4-x²) Then you get a "normal" integral, that you could integrade with respect to x. --> Area = ∫ x²y(x) sqrt(1+y(x)'²) dx from 0..2 ∫ _0^2 x²sqrt( (4-x²))sqrt(4/(4-x²) ) dx = 16/3 But agreed, parametrization is more elegant. And more intuitively, if you associate 't' with timelike dimension. Greetings from Germany!
I think this is a bit different than the line integrals we normally do in physics. The work done, for example, by a force is the integral of F dot ds where F= and ds= (so, basically the vector equivalent of what was done here). The time when the equation you wrote would work is when the force is always in the direction of the curve itself.
Yeah, what you’re describing is the line integral of a vector field, here we’re talking about line integrals of functions. The two are related by integral F . dr is integral of F . r’(t)/|r’(t)| ds
I am studying civil engineering in the best construction school in Mexico. Hope all the math courses teachers were as good as you bro. Please make a video explaining how do PDE work. Don't need them but I always want to learn more advanced calculus.
There is possibly a lot of version for this line integral... Would integrating infinitely thin sheet density give any mass? Maybe that should have an example case... This seems to work very well with circular arc cases, where the square root term is canceling out and possibly quite well with straight line cases as y=x, y=c1 or x=c2... This looks quite a good example case. Taking f(x,y)=h would give test case to compare with cylinders surface area A=theta*sqrt(x0^2+y0^2)*h=theta*r*h... If h
It's very convenient to integrate a curve on the basis of it's parametric function. But what if a curve is unrepresentable by any explict parametric function of x and y, and only defines a relationship between them instead? (like ln(x+y)-sin(xy)+3=0 and given a range and a function f defined on XY plane)
Hi Dr. Peyam, awesome like always, I would like you answer me a question, is it possible to apply the residue theorem to non definite integrals?, I have read books about Complex analysis but I never saw it, do you know where I can get info about it just in case it’s possible.
Dr peyam I am studying this concept in calculus based physics, however we are using only 1 dimension. Mostly to see how much a spring compresses. I had hard time with this in calc 3. So I have to retake that class... I can see the application for this in one dimension In two dimensions or three dimensions, is the line sort of moving along a path? Like a particle falling in the sky?
Can you do a line integral on something crazy like the Koch snowflake? In such a case its might not even make sense to call it a "line" integral, its not even one dimensional. Does it mean that the only way to get a meaningful answer out of it is to make ds log3(4) dimensional?
Interesting! I don’t think a Koch snowflake works because it’s not rectifiable. You could use Lebesgue integration with the measure being Hausdorff measure?
LOL: "WTF"..... who could imagine that calculus shows, that the "WTF" aka (area) is the mathematical inverse of "SLOPES". Areas and slopes are INVERSES.
@@callmedeno they are in analytic approach of calculus where you PLOT slopes dy/dx as fxn of x, compared to PLOTS of original fxn Y(x). In this analytic frame, it's beginner calculus, slopes and areas are inverse to each other. (In reality, it's subtraction which produces dy/dx from y, and addition which produces y from dy/dx)
Holy shit I knew there was something to the trigonometric interpretation of the derivative the derivative of a function f is the tangent of the angle opposite of the small change in y dy and the 2nd derivative is the derivative of the tangent of this angle which is sec^2(theta) the derivative is represented by a point made by the tangent line the 2nd derivative is made from 3 points the 2 intersecting the secant line and the point in between them this creates a parabola in which there are 2 angles needed to represent it the amount of points needed to express the degree n of a derivative onto the function f(x) is 2n - 1 while the amount of angles needed to express degree n is 2^(n - 1) this can be expanded into higher dimensions this is also why no function increases faster than x = a where a is a constant because the angle theta has a boundary condition of being undefined at pi/2 because that would not be a triangle there would be more than one right angle the absolute value of the difference between angle dx and dy has to be greater than 0 by the definition of a triangle this means you could polarize the derivative in terms of theta by taking the inverse tangent of the derivative
Math would be a piece of cake if all of our math teachers were as happy as this man.
Well said. 👏 👏 👏
Math is easy for the most part. It just requires time and interest - which most people can't put in.
Want to find
That’s definitely what wtf means
When I was in an undergrad class I learned wwts, meaning 'we want to show'. It was new to me at the time, but I have used it since with my own students. Looking at current abbreviations, I think it works better than what Dr. Peyam uses here which is distracting to students.
I love how I'm not the only person that was completely thrown by 'wtf' hahaha! Absolutely love the dedication and quality content Dr. Peyam we do not deserve such an amazing prof. like you!!!
My calc teacher gave a good intuition for line integrals. ds becomes ||T'||dt because it's the speed*time, so you get a tiny distance. The function is at a certain height, so distance*distance is area. Adding all the tiny distances together you get the integral.
Same sort of things for vector line integrals, except it's
F•ds = F•T'dt.
I like that!
Love the "wtf" lmao
the best explanation of line integral I've ever seen
Thank you!!!
Perfectly clear ! Thank you for this bright explanation.
Hey man just wanna appreciate your work, I have been watching your videos since I was in secondary school now I'm about to pass out of college and still proceed to watch your videos with same enthusiasm whenever it pops up in recommendation, just can't resist watching.
Thanks so much!!!
Calculus *is* WTF!
You did it again, you made it look so simple! Thanks!!
Alternatively, you could also express y in terms of x. --> y(x) = sqrt(4-x²)
Then you get a "normal" integral, that you could integrade with respect to x. --> Area = ∫ x²y(x) sqrt(1+y(x)'²) dx from 0..2
∫ _0^2 x²sqrt( (4-x²))sqrt(4/(4-x²) ) dx = 16/3
But agreed, parametrization is more elegant. And more intuitively, if you associate 't' with timelike dimension. Greetings from Germany!
Parameterisation wird auch wegen Gewohnheit gemacht. Wenn die Funktionen schwieriger werden, kann es nützlicher sein
You are amazing Peyam, greeatings from Manaus, Brazil ! ( você é o cara!)
I think this is a bit different than the line integrals we normally do in physics. The work done, for example, by a force is the integral of F dot ds where F= and ds= (so, basically the vector equivalent of what was done here). The time when the equation you wrote would work is when the force is always in the direction of the curve itself.
Yeah, what you’re describing is the line integral of a vector field, here we’re talking about line integrals of functions. The two are related by integral F . dr is integral of F . r’(t)/|r’(t)| ds
Precioso ejemplo, simple, claro...etc...etc. Muchas Gracias.
I am studying civil engineering in the best construction school in Mexico. Hope all the math courses teachers were as good as you bro. Please make a video explaining how do PDE work. Don't need them but I always want to learn more advanced calculus.
There’s already a playlist on that
Your video is great. I just back to watch it for the 3rd time, but with taking notes.
Glad you enjoyed it!
Great video Dr Peyam, but how do you go from this to Laurent series and Cauchy's residue theorem?
Thanks! Your video helps alot
Excelente video Doc.
I liked this video a lot because u simplified all of it to the point first year engineer student understood it.🤗
LOL this is in my exam and I am first year engineer student
There is possibly a lot of version for this line integral... Would integrating infinitely thin sheet density give any mass? Maybe that should have an example case...
This seems to work very well with circular arc cases, where the square root term is canceling out and possibly quite well with straight line cases as y=x, y=c1 or x=c2...
This looks quite a good example case. Taking f(x,y)=h would give test case to compare with cylinders surface area A=theta*sqrt(x0^2+y0^2)*h=theta*r*h...
If h
The PI - M method; picture, inequality, math. By doctor Peyam.
You are a genius.
Awwwww
It's very convenient to integrate a curve on the basis of it's parametric function. But what if a curve is unrepresentable by any explict parametric function of x and y, and only defines a relationship between them instead? (like ln(x+y)-sin(xy)+3=0 and given a range and a function f defined on XY plane)
Linear density of wire C, right?
Idea for a fun (challenging?) youtube video -- solving the following integral: (0 --> +inf) sin(x*e^x)/(x*e^x)
Sir, how to find the line integral formula and how to relate it with the graphical diagram.Can u make a video on it.:(India)
It’s on my playlist
Waiting for the next video !
Aplications on physics.Its so exciting.
Very useful video! Could you do the same for flux and also for line and flux integrals in space? Thanks!
Very interesting, thank you.
Nice Video and greetings from Germany
Hallo 😄
Hallo🤗
It would be fantastic if you can make a video about differential forms!
I’m considering it! Need to learn all of differential geometry now :)
Hi Dr. Peyam, awesome like always, I would like you answer me a question, is it possible to apply the residue theorem to non definite integrals?, I have read books about Complex analysis but I never saw it, do you know where I can get info about it just in case it’s possible.
This is where I could find it: th-cam.com/video/VZL6QFyMcf8/w-d-xo.html
For that last note about f as density, that interpretation is used for statistical distributions, and so it's used in machine learning and AI.
Interesting!
Dr peyam
I am studying this concept in calculus based physics, however we are using only 1 dimension.
Mostly to see how much a spring compresses.
I had hard time with this in calc 3. So I have to retake that class...
I can see the application for this in one dimension
In two dimensions or three dimensions, is the line sort of moving along a path? Like a particle falling in the sky?
Yeah it’s a particle moving on a path in 2d or 3d
@@drpeyam so it doesn't have to be a straight line?
Sir, can you please explain to me what is the line integral in Green's theorem. It has Pdx+Qdy, which is completely different than this, I don't know.
Check out my video on green’s theorem
Brilliant 🔥
Thank you so much :)
Could you do the inverse function of the gamma function?
Great pal, kind regards
Just a quick question to Dr Peyam: does UCI have a break tomorrow?
Yeah
@@drpeyam That's nice. How sad that Cal Poly Pomona doesn't.
You can do an math analysis course
Thank you so much
Definitely WTF more videos of yours
thanks, subscribed
Yay, thank you!!!
Can you do a line integral on something crazy like the Koch snowflake?
In such a case its might not even make sense to call it a "line" integral, its not even one dimensional.
Does it mean that the only way to get a meaningful answer out of it is to make ds log3(4) dimensional?
Interesting! I don’t think a Koch snowflake works because it’s not rectifiable. You could use Lebesgue integration with the measure being Hausdorff measure?
Thanks.
Thank you
Thank you very much on your videos, and love your abbreviation WTF xD.
Thanks man
I'll never understand why he says "Thanks for watching" before the video starts.
@Astronaut Posts Makes sense
LOL: "WTF"..... who could imagine that calculus shows, that the "WTF" aka (area) is the mathematical inverse of "SLOPES". Areas and slopes are INVERSES.
are areas and slopes really inverses or are they just the results of inverse operations?
@@callmedeno they are in analytic approach of calculus where you PLOT slopes dy/dx as fxn of x, compared to PLOTS of original fxn Y(x). In this analytic frame, it's beginner calculus, slopes and areas are inverse to each other. (In reality, it's subtraction which produces dy/dx from y, and addition which produces y from dy/dx)
13:52 Yes, you are live and not just talking to yourself.
Oooooh “want to find”… 😂 I thought the acronym stood for something else… also accurate though 😀👍
Dr:We want To Find (WTF)
Me: wtf!😅
Nice!
barikala!!! im from tehran. narmak
Do you think that you'd ever do a video on differential forms or the exterior derivative?
Eventually
@@drpeyam can you do video on exterior products
8:24 C-Señor!! :)
PIEM (Peyam) METHOD: Picture, InEquality, Maths
RDVMusic 😐
What happened to your buddy blackpenredpen?
He’s fine :)
Is that a bonobos shirt? I think some of their shirts are cool, but everyone recognizes them now.
Also Dr peyam are you aware your content is made for kids so we don't get notified if you make new content?
I marked it not safe for kids
Holy shit I knew there was something to the trigonometric interpretation of the derivative the derivative of a function f is the tangent of the angle opposite of the small change in y dy and the 2nd derivative is the derivative of the tangent of this angle which is sec^2(theta) the derivative is represented by a point made by the tangent line the 2nd derivative is made from 3 points the 2 intersecting the secant line and the point in between them this creates a parabola in which there are 2 angles needed to represent it the amount of points needed to express the degree n of a derivative onto the function f(x) is 2n - 1 while the amount of angles needed to express degree n is 2^(n - 1) this can be expanded into higher dimensions this is also why no function increases faster than x = a where a is a constant because the angle theta has a boundary condition of being undefined at pi/2 because that would not be a triangle there would be more than one right angle the absolute value of the difference between angle dx and dy has to be greater than 0 by the definition of a triangle this means you could polarize the derivative in terms of theta by taking the inverse tangent of the derivative
is he Young Sheldon
🤣🤣🤣🤣🤣🤣
Definitely had a dimebag.
so that's what wtf means :O literally wtf?
Go raibh míle maith agat
WTF UNDER F AND OVER C?!
Yep
WTF!!!!
WTF? 😂
wtf